The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations
A.A. Alderremy,Hassan Khan,Rasool Shah,Shaban Aly,Dumitru Baleanu +4 more
- Vol. 8, Iss: 6, pp 987
Reads0
Chats0
TLDR
In this paper, the analytical solution of Fornberg-whitham equations in fractional view of Caputo operator is dealt with and the effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems.Abstract:
This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.read more
Citations
More filters
Journal ArticleDOI
New Perspective on the Conventional Solutions of the Nonlinear Time-Fractional Partial Differential Equations
TL;DR: Numerical results for different cases of the fractional-order are presented graphically, which show the effectiveness of the proposed procedure and revealed that the proposed scheme is very effective, suitable for fractional PDEs, and may be viewed as a generalization of the existing methods for solving integer and noninteger order differential equations.
Journal ArticleDOI
A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law
TL;DR: In this paper , the authors applied efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg-de Vries equations with the Atangana-Baleanu fractional derivative.
A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law
TL;DR: In this paper , the authors applied modified decomposition method and new iterative transformation method to analyze a nonlinear system of Korteweg-de Vries equations with the Atangana-Baleanu fractional derivative.
Journal ArticleDOI
An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method
Hajira,Hassan Khan,Hassan Khan,Adnan Khan,Poom Kumam,Poom Kumam,Dumitru Baleanu,Muhammad Arif +7 more
TL;DR: In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier-Stokes equations with a Caputo fractional derivative, and numerical simulations and examples are presented to show the validity of the suggested method.
Journal ArticleDOI
An approximate analytical view of physical and biological models in the setting of Caputo operator via Elzaki transform decomposition method
TL;DR: In this article , a well-organized and novel algorithm for solving time-fractional Fornberg-Whitham, Klein-Gordon equation and biological population models occurring from physics and engineering is presented.
References
More filters
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI
An integrable shallow water equation with peaked solitons
Roberto Camassa,Darryl D. Holm +1 more
TL;DR: A new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution is derived.
A numerical and theoretical study of certain nonlinear wave phenomena
Bengt Fornberg,G. B. Whitham +1 more
TL;DR: In this article, an efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations, using a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time.
Journal ArticleDOI
Variational Methods and Applications to Water Waves
TL;DR: In this article, the authors review various uses of variational methods in the theory of nonlinear dispersive waves, with details presented for water waves, and show how more general dispersive relations can be formulated by means of integro-differential equations; an important application of this is towards resolving longstanding difficulties in understanding the breaking of water waves.
Journal ArticleDOI
On the concept of solution for fractional differential equations with uncertainty
TL;DR: In this article, the authors consider a differential equation of fractional order with uncertainty and present the concept of solution, which extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty.
Related Papers (5)
The Comparative Study for Solving Fractional-Order Fornberg–Whitham Equation via ρ-Laplace Transform
A numerical investigation of time-fractional modified Fornberg-Whitham equation for analyzing the behavior of water waves
S. Saha Ray,Arun Kumar Gupta +1 more